I won’t say anything about gravitational waves, but in EM, what you just said is unrelated, totally is related. If you just take the rules for electrostatics and the magnetic field from charges, and apply time-retardation, you recover the electromagnetic waves produced by that charge’s motion. No corrections or adjustments are needed.
That’s true, but that’s waves, not static attraction. In essence, electric attraction is “magically” corrected for the straight-line motion, so the electric field from a moving but non-accelerating charge points exactly in the direction of the charge, not in the direction where the charge was after accounting for time-retardation. This breaks down once you add acceleration, hence EM waves. The original post made this (possibly deliberate) mistake: calculated retarded field for (nearly) uniform motion when calculating the direction of the attractive force. Unless I misunderstood it.
For gravity the corrections resulting in radiation appear even later, its “predictive power” is one order in time derivatives better than that of EM.
I don’t recall the name, but here is a neat java applet visualizing the situation. In essence, for uniform motion the field lines are always straight, pointing away from the charge, while the direction of light received from the charge points to the retarded position. There is a standard detailed calculation (like the one in Griffiths or Jackson) here, with the following conclusion:
which confirms that the electric field at R points along the direction from R to the present (not the retarded) position of the charge.
But it still doesn’t change the causal relationship: that alignment only applies if nothing happens to the other thing in the time since the center of that retarded cone. If no new information has been generated, then sure, you can use the new information instead of the old information. But if anything happens, you had better use the old information!
To get more formal about it:
Consider or charge (equivalently, a mass) whose worldline coincides with (t, 0,0,0) for all t ⇐ 0) in some reference frame
The field at the event (10, 10, 0, 0 ) occurs after (0,0,0,0) in every subluminal reference frame.
The field at (10, 10, 0, 0 ) is independent of whatever happens at (1, 0,0,0). If a laser comes in and knocks that charge aside, there’s zero difference. None at all.
Suppose the charge was deflected so that it passes through (10, 1, 0, 0). You can’t get the electrical field at event (10, 10, 0, 0) by looking at what the charge is doing at (10, 1, 0, 0) - you need to look at (0,0, 0,0).
This is what causality looks like. The causal influences propagate at lightspeed. Even electrostatic ones.
But it still doesn’t change the causal relationship: that alignment only applies if nothing happens to the other thing in the time since the center of that retarded cone.
Absolutely. As I said
This breaks down once you add acceleration, hence EM waves.
However I am not sure I agree with the part in bold:
This is what causality looks like. The causal influences propagate at lightspeed. Even electrostatic ones.
When you say “Suppose the charge was deflected”, you have broken the electrostatic assumptions, since the charge is now accelerating. Depending on the distance, you either get the near-field effects or the radiative effects, which do indeed propagate at lightspeed. Once the acceleration disappears and the light-speed transients died down, you are back in the electrostatic/magnetostatic mode with lag-free fields.
That was the point of the example—by time 10, the charge was no longer accelerating, but you know that you’re not clear to use electrostatics being ‘noncausal’ yet because the light cone hasn’t reached that far. Being lag free is a computational convenience that sometimes applies, and you need to know when by applying causality.
So, it is ALWAYS fair to say that fields are causal influences, whether they’re static or dynamic. That was why I objected to your complaint in the first place.
Not necessarily. This is somewhat counter-intuitive, but the light lags the direction of the Coulomb’s law’s attraction if a charge moves past you with a constant velocity (and has been doing so for some time). The attraction force points to the “true” direction of the charge, whereas light takes a bit to catch up.
Note that this apparent FTL effect cannot be used to transmit any information FTL, because, as soon as you try to wiggle the charge to telegraph something, this wiggling will only be sent as EM radiation (light), at light speed.
So, it’s possible for the electrical force to act from a location that never had a charge? If the charge moves at a constant speed long enough and then makes a hard turn away, the charge will act on other objects (at least briefly) as if the charge had continued straight? Does the charge also act on the object as though it had not turned, even after it had, or is the force unilateral?
Yes to the second, not sure how the third is different. That’s why, in part, Newton’s second law does not in general hold for Electromagnetism, but momentum conservation does, if you account for the momentum of the electromagnetic field itself.
That behavior is contrary to naive expectations, right? If I run really fast towards a wall but turn before I reach it, I shouldn’t hit it. It also shouldn’t smash my face in after I make the turn.
The major force involved in billiard balls bouncing off of each other is electric in nature, right?
That’s true, but that’s waves, not static attraction. In essence, electric attraction is “magically” corrected for the straight-line motion, so the electric field from a moving but non-accelerating charge points exactly in the direction of the charge, not in the direction where the charge was after accounting for time-retardation. This breaks down once you add acceleration, hence EM waves. The original post made this (possibly deliberate) mistake: calculated retarded field for (nearly) uniform motion when calculating the direction of the attractive force. Unless I misunderstood it.
For gravity the corrections resulting in radiation appear even later, its “predictive power” is one order in time derivatives better than that of EM.
Wat. This is so severely counterintuitive I’m going to have to look it up and get a technical explanation. Is there a named effect for this?
I don’t recall the name, but here is a neat java applet visualizing the situation. In essence, for uniform motion the field lines are always straight, pointing away from the charge, while the direction of light received from the charge points to the retarded position. There is a standard detailed calculation (like the one in Griffiths or Jackson) here, with the following conclusion:
Very interesting...
But it still doesn’t change the causal relationship: that alignment only applies if nothing happens to the other thing in the time since the center of that retarded cone. If no new information has been generated, then sure, you can use the new information instead of the old information. But if anything happens, you had better use the old information!
To get more formal about it: Consider or charge (equivalently, a mass) whose worldline coincides with (t, 0,0,0) for all t ⇐ 0) in some reference frame
The field at the event (10, 10, 0, 0 ) occurs after (0,0,0,0) in every subluminal reference frame.
The field at (10, 10, 0, 0 ) is independent of whatever happens at (1, 0,0,0). If a laser comes in and knocks that charge aside, there’s zero difference. None at all.
Suppose the charge was deflected so that it passes through (10, 1, 0, 0). You can’t get the electrical field at event (10, 10, 0, 0) by looking at what the charge is doing at (10, 1, 0, 0) - you need to look at (0,0, 0,0).
This is what causality looks like. The causal influences propagate at lightspeed. Even electrostatic ones.
Absolutely. As I said
However I am not sure I agree with the part in bold:
When you say “Suppose the charge was deflected”, you have broken the electrostatic assumptions, since the charge is now accelerating. Depending on the distance, you either get the near-field effects or the radiative effects, which do indeed propagate at lightspeed. Once the acceleration disappears and the light-speed transients died down, you are back in the electrostatic/magnetostatic mode with lag-free fields.
That was the point of the example—by time 10, the charge was no longer accelerating, but you know that you’re not clear to use electrostatics being ‘noncausal’ yet because the light cone hasn’t reached that far. Being lag free is a computational convenience that sometimes applies, and you need to know when by applying causality.
So, it is ALWAYS fair to say that fields are causal influences, whether they’re static or dynamic. That was why I objected to your complaint in the first place.
Isn’t “the direction of the charge” where you point a telescope to look at it, even if it is moving?
Not necessarily. This is somewhat counter-intuitive, but the light lags the direction of the Coulomb’s law’s attraction if a charge moves past you with a constant velocity (and has been doing so for some time). The attraction force points to the “true” direction of the charge, whereas light takes a bit to catch up.
Note that this apparent FTL effect cannot be used to transmit any information FTL, because, as soon as you try to wiggle the charge to telegraph something, this wiggling will only be sent as EM radiation (light), at light speed.
So, it’s possible for the electrical force to act from a location that never had a charge? If the charge moves at a constant speed long enough and then makes a hard turn away, the charge will act on other objects (at least briefly) as if the charge had continued straight? Does the charge also act on the object as though it had not turned, even after it had, or is the force unilateral?
Yes to the second, not sure how the third is different. That’s why, in part, Newton’s second law does not in general hold for Electromagnetism, but momentum conservation does, if you account for the momentum of the electromagnetic field itself.
That behavior is contrary to naive expectations, right? If I run really fast towards a wall but turn before I reach it, I shouldn’t hit it. It also shouldn’t smash my face in after I make the turn.
The major force involved in billiard balls bouncing off of each other is electric in nature, right?